What's the difference between the public transport types?

This question is mostly opinion based due to the nature of the game but based on facts, the biggest issue with monorails is noise pollution. Placing monorail tracks and stations in the middle of residential areas will increase noise pollution and cause a drop in health.

Regarding costs, take a look at the table below. As you can see, the differences are minor.

I cannot find a source but I read on reddit once that the monorail is faster on longer distances, but I cannot find any data to back it up.

For me it mostly comes down to aesthetics. Metro is mostly invisible but with the monorail you can put avenues with monorail tracks which sort of makes the city "prettier".

You can also have a look at the this reddit post about transportation, which might help you.